This is the first comprehensive monograph on a new thermodynamic theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the local equilibrium hypothesis is abandoned. The basic variables describing the system are no longer the equilibrium conserved variables: the latter are complemented by non-equilibrium quantities taking the form of flux heat, the viscous pressure tensor, the flux of matter, the flux of electric current, etc. The statements behind extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications such as hyperbolic heat conduction, rheological models, waves in fluids, generalized hydrodynamics, phase diagrams of solutions under shear, non-Fickian diffusion, electrical systems, and a relativistic formulation including some cosmological applications. The book also contains a wide discussion of the foundations and the scope of the most current theories on non-equilibrium thermodynamics (classical irreversible thermodynamics and rational thermodynamics). The new edition reflects new developments in theory and applications, adds new problems, and contains a new chapter on the interplay between hydrodynamics and thermodynamics, a field of active research.